Question

Im not the best at word problems A box of jerseys for a pick-up game of basketball contains 10 extra-large jerseys, 7 large jerseys, and 5 medium jerseys. If you are first to the box and grab 3 jerseys, what is the probability that you randomly grab 3 medium jerseys? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth

Answer 1

Given:

The number of extra-large jerseys is 10.

The number of large jerseys is 7.

The number of medium jerseys is 5.

Three jerseys to be taken.

To find the probability that randomly grabs 3 medium jerseys:

The probability is,

$\begin{gathered} P(E)=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \\ =\frac{^5C_3}{^{22}C_3} \\ =\frac{\frac{5!}{(5-3)!3!}}{\frac{22!}{(22-3)!3!}} \\ =\frac{\frac{5!}{2!3!}}{\frac{22!}{19!3!}} \\ =\frac{5\times4\times3}{22\times21\times20} \\ =\frac{1}{154} \end{gathered}$

Hence, the probability that randomly grabs 3 medium jerseys is,

$\frac{1}{154}$